The manager at a movie theater keeps track of the number of evening tickets and matinee tickets sold each day and the total money received. On Friday, a total of 63 tickets were sold, and the money collected was $742. If evening tickets are sold for $14 and matinee tickets are sold for $10, how many evening tickets and matinee tickets were sold?

Given:

63 tickets were sold.

Money collected = $742.

Evening tickets cost $14 each.

Matinee tickets cost $10 each.

Let

x = number of evening tickets sold

y = number of matinee tickets sold

Then

x + y = 63 (1)

14x + 10y = 742 (2)

From (1), obtain

y = 63 - x (3)

Substitute (3) into (2).

14x + 10 (63 - x) = 742

4x + 630 = 742

4x = 112

x = 28

y = 63 - 28 = 35

Answer: 28 evening and 35 matinee tickets were sold.